Information on Result #1427349
Linear OOA(4189, 4322, F4, 2, 40) (dual of [(4322, 2), 8455, 41]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4189, 4322, F4, 40) (dual of [4322, 4133, 41]-code), using
- 206 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 6 times 0, 1, 16 times 0, 1, 32 times 0, 1, 56 times 0, 1, 88 times 0) [i] based on linear OA(4182, 4109, F4, 40) (dual of [4109, 3927, 41]-code), using
- construction X applied to Ce(40) ⊂ Ce(37) [i] based on
- linear OA(4181, 4096, F4, 41) (dual of [4096, 3915, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(4169, 4096, F4, 38) (dual of [4096, 3927, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(41, 13, F4, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(40) ⊂ Ce(37) [i] based on
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(4189, 2161, F4, 3, 40) (dual of [(2161, 3), 6294, 41]-NRT-code) | [i] | OOA Folding | |